1. Field of the Invention
The present invention relates to a method for measuring thickness of an optical disc.
2. Description of the Related Art
Various recording media exist, such as a magnetic recording tape, a Laser Disc (LD) and a Compact Disc (CD) as optical discs, and a Digital Video Disc (hereinafter referred to as DVD) that have the capacity to record vast amounts of information. Since the optical disc, as compared with other recording media, utilizes a different digital recording system, is light weight, and is convenient to keep and carry, many users prefer the optical disc over other recording media.
Moreover, recording media are under development with higher density and higher integration. For example, a Blu-ray Disc (BD) as a High Density DVD (HD-DVD) has a higher integration than current DVDs.
As new optical discs are developed, methods for manufacturing these products are also being developed and improved. Production of a reliable and high quality optical disc presents unique challenges since minute signal characteristics associated with inferior quality may originate from errors in thickness of a disc, scratches, deformities, fingerprints, and attachment of foreign material to the optical disc during manufacturing of the product.
In particular, thickness variations of a disc is a major factor affecting product quality and reliability. Thus, it is necessary to measure the thickness in real time for processing control during manufacturing.
An optical disc may be treated in a manner similar to a thin film. If the thickness of the thin film is under several μm, the measurement of the thickness depends on a quantitative measurement such as a thin film analysis by ellipsometry and measurement of a reflection factor. If the thickness of a relatively thick thin film equal to or greater than several μm is analyzed, the thickness may be measured by a vibration period appearing in a reflective or transparent spectrum due to an interference effect.
The thickness of a thin film may be measured by obtaining a vibration period (or frequency) of the spectrum by the interference and determining the thickness of the thin film from the obtained vibration period. However, as thin films become thick, the time necessary to estimate the thickness of the thin film increases. In order to rapidly measure the thickness of thick thin films, a conventional Fast Fourier Transform (hereinafter referred to as “FFT”) is utilized as a rapid measurement of the vibration period of the spectrum.
FIG. 1 is a schematic of a conventional apparatus for measuring the thickness of a thin film.
As illustrated in FIG. 1, the apparatus measures the thickness of a thin film by measuring a reflectivity spectrum. Light from a halogen lamp 12 is projected on a substrate 30 with a thin film 32 through an optical fiber 22 and a lens 26, which is assigned in a perpendicular direction with respect to the recording surface of the optical disc. Light reflected from the substrate 20 is transmitted to a spectrograph 42 through the lens 26 and the optical fiber 24. The spectrograph 42 splits the light reflected from a surface of a sample on the substrate 30 according to the intensity of each wavelength. The split light is then directed to an optical measuring element arrangement 44 that supplies the luminance intensity at each wavelength to a computer 46. The computer 46 determines the thickness of the thin film using luminance intensity information at each wavelength as spectrum data.
FIGS. 2A and 2B are views illustrating how a refractive index may be used to determine the thickness of an optical disc measured by a conventional method. FIG. 2A is a graph showing a luminous intensity data spectrum at each wavelength according to the conventional method. FIG. 2B is a graph of a Fast Fourier Transform of the reflectivity spectrum based on the data of FIG. 2A.
As illustrated in FIGS. 2A and 2B, since Δλ can be selected, where Δλ is m times with respect to a specific wavelength α and m−1 times with respect to near wavelength λ+Δλ, the thickness d of a specific layer in the spectrum data according to the refractive index may be represented by the following equation 1.
At the condition Δλ<<λ,2nd=mλ=(m−1)(λ+Δλ), and if expanded,mλ=(m−1)(λ+Δλ)=mλ+mΔλ−(λ+Δλ)mΔλ=λ+Δλ  [Equation 1]
therefore, becomes m=(λ+Δλ)/Δλ,
where, 2nd=mλ=λ(λ+Δλ)/Δλ≈λ2/Δλ=1/λ(1/λ)
Since multiplication of 2nd and Δ(1/λ) is 1 (one), if, in the experiment, a relationship function between the reflectivity intensity and Δ(1/λ) can be obtained, an FFT function with respect the 2nd corresponding to transform factor of Δ(1/λ) by taking the FFT wholly.
Thus, a d value, where a peak appears, is the thickness to be determined.
For reference, the description for the FFT is represented to a generalized equation as follows.
A relationship equation between the intensity I and the wavelength λ becomesI=f(λ)=g(Δ(1/Δ)).
If applying the FFT to both sides, then the equation can be expressed as following equation 2.
                              FFT          ⁢                      {            I            }                          =                              FFT            ⁢                          {                              g                ⁡                                  (                                      Δ                    ⁡                                          (                                              1                        λ                                            )                                                        )                                            }                                =                                    ∫                                                g                  ⁡                                      (                                          Δ                      ⁡                                              (                                                  1                          λ                                                )                                                              )                                                  ⁢                                  ⅇ                                                            -                      2                                        ⁢                    π                    ⁢                                                                                  ⁢                                          i                      ⁡                                              (                                                  Δ                          ⁡                                                      (                                                          1                              λ                                                        )                                                                          )                                                              ⁢                    2                    ⁢                                                                                  ⁢                    nd                                                  ⁢                                  ⅆ                                      (                                          2                      ⁢                      nd                                        )                                                                        =                                          h                ⁡                                  (                                      2                    ⁢                                                                                  ⁢                    nd                                    )                                            .                                                          [                  Equation          ⁢                                          ⁢          2                ]            
However, since the conventional method does not consider the refractive index dispersion of thin film material, the gap between peaks decreases gradually. More especially, according to the conventional art, there are disadvantages since the refractive index is varied depending upon the wavelength, thickness values obtained according to the refractive index for dividing a Fourier peak position are varied and reduction of size and increment of a width of the peak are caused.
Thus, since the materials of an actual thin film have a wavelength dependant on the refractive index, that is, since there is a refractive index dispersion of the thin film, the energy difference caused by the interference between two lights at a frequency period is not uniform. For this reason, the width of the peak that is obtained using the Fast Fourier Transform from the reflective spectrum is wider according to the degree of the refractive index dispersion. Furthermore, the error in ascertaining the thickness of the thin film because of the imprecise position of the peak increases. Therefore, in order to precisely measure the thickness of the thin film, the refractive index dispersion should be considered.